Vanishing Viscous Limits for 3D Navier-Stokes Equations with a Navier-Slip Boundary Condition

In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in R³. We first obtain the higher order regularity estimates for the solutions to Prandtl's equation boundary layers. Furthermore, we prove that the strong solution to Navier-Stokes equations converges to the Eulerian one in C([0, T]; H¹(Ω)) and $${L^\infty((0,T) \times \Omega)}$$, where T is independent of the viscosity, provided that initial velocity is regular enough. Furthermore, rates of convergence are obtained also.